# simd_quatd A double-precision quaternion. ``` struct simd_quatd ``` ## Topics ### Initializing a quaternion [`init()`](/documentation/simd/simd_quatd/init()) Creates a new quaternion. [`init(vector:)`](/documentation/simd/simd_quatd/init(vector:)) Creates a new quaternion from a four-element vector. [`init(_:)`](/documentation/simd/simd_quatd/init(_:)-791zk) Creates a new quaternion from a 3 x 3 rotation matrix. [`init(_:)`](/documentation/simd/simd_quatd/init(_:)-5vcd5) Creates a new quaternion from a 4 x 4 rotation matrix. [`init(angle:axis:)`](/documentation/simd/simd_quatd/init(angle:axis:)) Creates a new quaternion with an action that’s a rotation about an axis. [`init(from:to:)`](/documentation/simd/simd_quatd/init(from:to:)) Creates a new quaternion with an action that’s a rotation between two vectors. [`init(ix:iy:iz:r:)`](/documentation/simd/simd_quatd/init(ix:iy:iz:r:)) Creates a new quaternion from four scalar values that specify the imaginary and real parts. [`init(real:imag:)`](/documentation/simd/simd_quatd/init(real:imag:)) Creates a new quaternion from a scalar real part and a vector imaginary part. ### Querying a quaternion’s properties [`angle`](/documentation/simd/simd_quatd/angle) The angle, in radians, by which the quaternion’s action rotates. [`axis`](/documentation/simd/simd_quatd/axis) The normalized axis about which the quaternion’s action rotates. [`conjugate`](/documentation/simd/simd_quatd/conjugate) The conjugate of the quaternion. [`imag`](/documentation/simd/simd_quatd/imag) The imaginary part of the quaternion. [`real`](/documentation/simd/simd_quatd/real) The real part of the quaternion. [`inverse`](/documentation/simd/simd_quatd/inverse) The inverse of the quaternion. [`length`](/documentation/simd/simd_quatd/length) The length of the quaternion. [`normalized`](/documentation/simd/simd_quatd/normalized) The unit quaternion of the quaternion. [`vector`](/documentation/simd/simd_quatd/vector) The underlying vector of the quaternion. ### Creating a quaternion from other data types [`simd_quaternion(_:_:_:_:)`](/documentation/simd/simd_quaternion(_:_:_:_:)-1adm9) Returns a new quaternion from 4 scalar values. [`simd_quaternion(_:_:)`](/documentation/simd/simd_quaternion(_:_:)-2jzvc) Returns a new quaternion from a scalar value and a three-element vector. [`simd_quaternion(_:)`](/documentation/simd/simd_quaternion(_:)-8kl4p) Returns a new quaternion from a pointer to scalar values. [`simd_quaternion(_:_:)`](/documentation/simd/simd_quaternion(_:_:)-2yoqw) Returns a new quaternion from 2 three-element vectors. [`simd_quaternion(_:)`](/documentation/simd/simd_quaternion(_:)-7paor) Returns a new quaternion from a 3 x 3 matrix. [`simd_quaternion(_:)`](/documentation/simd/simd_quaternion(_:)-459vs) Returns a new quaternion from a four-element vector. [`simd_quaternion(_:)`](/documentation/simd/simd_quaternion(_:)-8e0xf) Returns a new quaternion from a 4 x 4 matrix. ### Applying arithmetic operations to quaternions [`simd_add(_:_:)`](/documentation/simd/simd_add(_:_:)-6ohmq) Returns the sum of two quaternions. [`simd_mul(_:_:)`](/documentation/simd/simd_mul(_:_:)-531pe) Returns the product of two quaternions. [`simd_mul(_:_:)`](/documentation/simd/simd_mul(_:_:)-8aedk) [`simd_mul(_:_:)`](/documentation/simd/simd_mul(_:_:)-8uidm) [`simd_sub(_:_:)`](/documentation/simd/simd_sub(_:_:)-87caf) Returns the difference between two quaternions. [`exp(_:)`](/documentation/simd/exp(_:)-9nl1f) [`log(_:)`](/documentation/simd/log(_:)-77xdo) ### Applying geometric operations to quaternions [`simd_act(_:_:)`](/documentation/simd/simd_act(_:_:)-47h09) Returns a vector rotated by a quaternion. [`act(_:)`](/documentation/simd/simd_quatd/act(_:)) Returns the specified vector rotated by the quaternion. [`simd_angle(_:)`](/documentation/simd/simd_angle(_:)-zuvx) Returns the angle by which a quaternion rotates. [`simd_axis(_:)`](/documentation/simd/simd_axis(_:)-56wf4) Returns the normalized axis about which the action of the specified quaternion rotates. [`simd_bezier(_:_:_:_:_:)`](/documentation/simd/simd_bezier(_:_:_:_:_:)-556xd) Returns the spherical cubic Bezier interpolation between quaternions. [`simd_conjugate(_:)`](/documentation/simd/simd_conjugate(_:)-98awl) Returns the conjugate of a quaternion. [`simd_imag(_:)`](/documentation/simd/simd_imag(_:)-2c7fz) Returns the imaginary (vector) part of a quaternion. [`simd_negate(_:)`](/documentation/simd/simd_negate(_:)-3ysgu) Returns the negation of a quaternion. [`simd_real(_:)`](/documentation/simd/simd_real(_:)-75t5f) Returns the real (scalar) part of a quaternion. [`simd_slerp(_:_:_:)`](/documentation/simd/simd_slerp(_:_:_:)-65dt5) Returns a spherical linearly interpolated value along the shortest arc between two quaternions. [`simd_slerp_longest(_:_:_:)`](/documentation/simd/simd_slerp_longest(_:_:_:)-8hbz2) Returns a spherical linearly interpolated value along the longest arc between two quaternions. [`simd_spline(_:_:_:_:_:)`](/documentation/simd/simd_spline(_:_:_:_:_:)-19wbg) Returns an interpolated value between two quaternions along a spherical cubic spline. [`simd_dot(_:_:)`](/documentation/simd/simd_dot(_:_:)-2bnqp) Returns the dot product of two quaternions. [`dot(_:_:)`](/documentation/simd/dot(_:_:)-438xp) [`simd_length(_:)`](/documentation/simd/simd_length(_:)-52o29) Returns the length of a quaternion. [`simd_normalize(_:)`](/documentation/simd/simd_normalize(_:)-ud11) Returns a quaternion pointing in the same direction as the supplied quaternion with a length of 1. ### Inverting a quaternion [`simd_inverse(_:)`](/documentation/simd/simd_inverse(_:)-3cvvi) Returns the inverse of a quaternion. ### Providing a hash value [`hash(into:)`](/documentation/simd/simd_quatd/hash(into:)) Hashes the essential components of this value by feeding them into the given hasher. --- Copyright © 2026 Apple Inc. All rights reserved. | [Terms of Use](https://www.apple.com/legal/internet-services/terms/site.html) | [Privacy Policy](https://www.apple.com/privacy/privacy-policy)